Gauge-Yukawa theories: Beta functions at large $N_f$

TL;DR

This paper analyzes the renormalization group flow of gauge-Yukawa theories with many matter fields, revealing fixed points and phase structures relevant for extensions of the standard model, especially in the large N_f limit.

Contribution

It computes leading 1/N_f Yukawa and quartic beta functions in gauge-Yukawa theories with multiple matter fields, extending previous results and exploring their phase diagrams.

Findings

Identification of interacting ultraviolet fixed points.

Rich phase diagram with asymptotically safe fixed points.

Extension of beta function calculations beyond perturbation theory.

Abstract

We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semi-simple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the leading $1/N_f$ Yukawa and quartic beta functions. Our work elucidates, consolidates and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.